Crisis Core Final Fantasy VII Reunion - How to raise Buster Sword proficiency fast

Buster Sword is obtained during the story in Chapter 6. When you initiate a fight, look on the right, there is a "Proficiency..." label. The only way to raise it is to press X + Square button, and then attack either with regular attack or some skill (yellow) materia.

The ways to raise proficiency

Action -> Proficiency Gained
Guard Succesfully during Battle Stance -> 0.07%
(Goes up by 0.01% each time)
Battle Stance  -> Strong Attack    0.25%
(0.02-0.03% Per Enemy)
Battle Stance -> Use Command Materia    0.25%
(0.02-0.03% Per Enemy)

Proficiency unlocks

Profeciency -> Unlocked Ability
10~15％ -> Damage Limit Break
Damage threshold from Strong Attacks during Battle Stance will increase from 9999 to 99999.
55％ - 70% -> Barrier Piercing
Attacks ignore the effects of Barrier when dealing DMG.
70% - 85％ -> Barrier Break
Attacks take down the effects of Barrier when dealing DMG.
100％ -> No Ability Acquisition

The best and the easiest way is the Training mission under 1-1-2 with 50 enemies. I started with Jump materia, with ATK++, HP++, Quake. You can also prepare some other materia you want to level up along the way. Now, the max you can raise the proficiency is 0.57% per battle. That means you will soon hit that mark in the mentioned mission - that is why you also have quake to easily kill the enemies when your proficency stops growing. You can't just spam yellow skills like jump - half of those 0.57% comes from killing enemies with regular attacks while in stance mode + the remaining 0.07% for guarding while in battle stance mode. I combined this step with leveling up Goblin punch materia, as much ATK+, HP+, MAG+, MP+ materias I had - to fuse them later when you cross the 9999 limits. 

Repeating the mentioned missions is a great way to level up fast at the point of the game after beating the game, and just before you do the rest of the missions you might've been too weak to try.